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Question

A person standing on an open ground hears the sound of a jet aeroplane coming from north at an angle 60 with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, then speed of the plane is

A
32v
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B
v
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C
2v3
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D
v2
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Solution

The correct option is D v2
Let vP and v be the speed of the plane and speed of the sound.
Let P1 be the position of plane at t=0,
when sound waves started towards person A, P2 is the position of plane observed at time instant t as shown in the figure below.

In triangle P1P2A.
P1P2 = speed of plane × time =vP×t
P1A = speed of sound × time =v×t
Now, from ΔP1P2A,
cos60=P1P2P1A=vP×tv×t
12=vPv
vP=v2

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